What does a statevector with 3 elements (in Qiskit) represent?

What does a statevector with 3 elements (in Qiskit) represent? Ask Question Asked 4 years, 2 months ago Modified yesterday Viewed 412 times 1 I wasn't quite sure where to post this as I don't know if this is a Qiskit specific thing or not, but I'm not sure how to interpret this result I got from running a simulation. from result.data(): {'counts': {'0x0': 371, '0x1': 653}, 'statevector': [[0.6095190950364658, 0.00167238253077826], [0.6389605613454776, 0.46926856185163585], [0.0002864410240029574, -0.00010852146395313456]]} From result.get_statevector(): array([6.09519095e-01+1.67238253e-03j, 6.38960561e-01+4.69268562e-01j, 2.86441024e-04-1.08521464e-04j]) This is a 1-qubit system btw Also, I'm pretty new to QC, so pls be nice Here's the code I'm using to simulate the system: backend_sim = FakeArmonk() custom_gate = Gate('custom_gate', 1, []) qc1 = QuantumCircuit(1, 1) qc1.initialize([np.cos(a[0]/2), np.exp(a[1]*1.j)*np.sin(a[0]/2)], 0) qc1.append(custom_gate, [0]) qc1.measure(0, 0) with pulse.build(backend_sim, name='custom_gate') as my_schedule: pulse.play(Gaussian(duration=256+64, amp=.36, sigma=80), pulse.drive_channel(0)) qc1.add_calibration(custom_gate, [0], my_schedule) qc1 = transpile(qc1, backend_sim) pulse_sched = schedule(qc1, backend_sim) pulse_sched.draw() job1 = execute(pulse_sched, backend_sim, shots=1024) result1 = job1.result() result1.data() The initialize state doesn't matter, it is a random pure state, and the parameters of the Gaussian pulse are also arbitrary qiskitprogrammingsimulation Share Improve this question Follow edited Dec 20, 2021 at 0:43 3yakuya 6823 3 silver badges 10 10 bronze badges asked Dec 19, 2021 at 20:47 soravoid 814 4 bronze badges Add a comment 1 Answer Sorted by: Highest score (default) Date modified (newest first) Date created (oldest first) 0 From Qiskit docs: Statevector backends return a dictionary with key ‘statevector’ and values being a list[list[complex components]] list of 2^num_qubits complex amplitudes. Where each complex number is represented as a 2 entry list for each component. For example, a list of [0.5+1j, 0-1j] would be represented as [[0.5, 1], [0, -1]]. which gets perhaps a bit clearer in your result from get_statevector(), where you just got an array of 3 complex values. As for why 3 and not 2, docs on Statevector dimensions can be helpful: the length of the input vector specifies the total dimension of the density matrix. If it is a power of two the state will be initialized as an N-qubit state. If it is not a power of two the state will have a single d-dimensional subsystem. In other words, the resulting state is a mixed state (not pure.) Possibly helpful post on mixed states Share Improve this answer Follow answered Dec 19, 2021 at 21:51 3yakuya 6823 3 silver badges 10 10 bronze badges That's good to know! Tbh I didn't think a single qubit system could be mixed, but my perception of mixed and pure states are probably still off. Do you know of a way to get the density matrix out of the simulator (FakeArmonk)? Trying to get a density matrix from that statevector gives a 3x3 matrix. My ultimate goal is to check the fidelity of the final state with a pure state. –  soravoid Commented Dec 20, 2021 at 0:22 1 A single qubit state can be mixed, but even then the density matrix would be 2x2. I suspect that in this case, the statevector contains not only the amplitudes for the |0> and |1> state, but also for the |2> state. On a real system, the higher energy levels are also populated a bit and since you're working with pulses it might return also higher excited states? –  Cryoris Commented Dec 20, 2021 at 15:13 I think you're right, the numbers seem to be matching up, though the question now is whether I calculate the fidelity by excluding the probabilities in the |2> state or by making the coefficient 0 for |2> in the pure state –  soravoid Commented Dec 20, 2021 at 18:14 Add a comment Your Answer Sign up or log in Sign up using Google Sign up using Email and Password Post as a guest Name Email Required, but never shown Post Your Answer By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions qiskitprogrammingsimulation See similar questions with these tags. 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